Two-dimensional and one-dimensional models are used to evaluate the seashore effects of the tsunami generated by an asteroid hitting the deep water in the Eastern region of the Black Sea. The shallow water theory has been used to describe tsunami propagation. The distance between the impact point and the nearest coast is about 150 km. The effects on the coastal regions depend on many factors among which the most important is asteroid size. The tsunami generated by a 250 m asteroid reaches the nearest dry land location in 20 minutes and needs about two hours to hit all over the Black Sea coast. The horizontal inundation length is also known as run-in or run-off distance, according to the direction of water movement. The run-up values may be up to 39 m in the Eastern basin and a more than ten times smaller in theWestern region. The Northern part of the Black Sea coast is not affected by the tsunami. The run-in values of a tsunami generated by a 1000 m diameter asteroid are sensibly larger than the similar values associated to a 250 m diameter asteroid. The run-in strongly depends on the distance from the impact position to the shore and on coastal topographical profile. For instance, the run-in distance in case of a tsunami generated by a 250 m size asteroid is 0.1 km (at Varna), 0.5 km (Ordu), 0.7 km (Yalta) and 1.4 km (Sochi). In case of the 1000 m diameter asteroid the run-in distance is 0.7 km (at Varna) and 2.9 km (Yalta). The results accuracy is also discussed.